How can I draw a parallel line to other edge in a face?
There are a few methods, but usually the most intuitive is the knife tool. Put your view in orthographic and snap it so that the line you want to cut is either flat horizontal or vertical and use the angle constraint mode (c).

If there are things blocking your view of the cut just hide them (h). If the cut isn't aligned to one of the global axes then you can select a face with a parallel edge and snap you view to it with shift+numpad7/1/3.

In the case you have drawn though, I would just use the knife tool and cut the edge without worrying about getting it parallel. After the edge is cut grab the vertex at 'g', enable vertex snapping and constrain movement to z axis. Then snap it to the vertex at 'f'.